Question 820967: Find the exact value of cos n/4
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Maybe you meant  .
The whole circle,  is  measured in radians,
so  is  , a right angle.
A square has 4 congruent sides (equal length) and 4 right angles.
A diagonal divides a square into two isosceles right triangles,
with a right angle ( otr  ,
and two congruent (equal measure) angles,
measuring  or  .
The trigonometric functions of such an angle can be calculated as the ratios of the sides of such a triangle.
If I make the length of the sides of my square  unit (of whatever unit you want), how long is that diagonal
 The diagonal is the hypotenuse of a right triangle with legs measuring .
The length of the diagonal is  .
The sine of one of those angles is the ratio of opposite leg, divided by hypotenuse, so
However, we do not like to see square roots in denominators, so we multiply numerator and denominator times  .
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